Question

Phân tích đa thức thành nhân tử: 2x^4+5x^3+13x^2+25x+15

 

Answer 1

\(\text{e) 2x^4 + 5x^3+13x^2+25x+15 }\)
  \(\text{=2x^3(x+1)+3x^2(x+1)+10x(x+1)+15(x+1) }\)
  \(\text{=(x+1)[x^2(2x+3)+5(2x+3)]}\)
  \(\text{=(x+1)(2x+3)(x^2+5)}\)

Answer 2

\(2x^4+5x^3+13x^2+25x+15\)

\(=2x^4+2x^3+3x^3+3x^2+10x^2+10x+15x+15\)

\(=2x^3\left(x+1\right)+3x^2\left(x+1\right)+10x\left(x+1\right)+15\left(x+1\right)\)

\(=\left(x+1\right)\left(2x^3+3x^2+10x+15\right)\)

Answer 3

Làm tiếp

\(=\left(x+1\right)\left[x^2\left(2x+3\right)+5\left(2x+3\right)\right]\)

\(=\left(x+1\right)\left(2x+3\right)\left(x^2+5\right)\)

Answer 4

\(2x^4+5x^3+13x^2+25x+15\)

\(=2x^4+2x^3+3x^3+3x^2+10x^2+10x+15x+15\)

\(=\left(2x^4+2x^3\right)+\left(3x^3+3x^2\right)+\left(10x^2+10x\right)+\left(15x+15\right)\)

\(=2x^3\left(x+1\right)+3x^2\left(x+1\right)+10x\left(x+1\right)+15\left(x+1\right)\)

\(=\left(x+1\right)\left(2x^3+3x^2+10x+15\right)\)

\(=\left(x+1\right)\left[\left(2x^3+10x\right)+\left(3x^2+15\right)\right]\)

\(=\left(x+1\right)\left[2x\left(x^2+5\right)+3\left(x^2+5\right)\right]\)

\(=\left(x+1\right)\left(2x+3\right)\left(x^2+5\right)\)